#### Question

# Given: Δ ABC. A = 100, a = 125, c = 10. Find the remaining side lengths and angle measures.?

please help!

#### Answers

Using the Law of Sines, we can find C:

sin(A)/a = sin(C)/c

==> sin(100°)/125 = sin(C)/10

==> sin(C) = (10/125)sin(100°) = (2/25)sin(100°)

==> C = arcsin[(2/25)sin(100°)] ≈ 4.5°.

(Since A is obtuse, we do not have to worry about the ambiguous case.)

Since the three angles of a triangle add up to 180°, we see that:

A + B + C = 180° ==> B = 180° - A - C = 180° - 100° - 4.5° = 75.5°.

Then, using the Law of Sines to find b:

sin(A)/a = sin(B)/b

==> sin(100°)/125 = sin(75.5°)/b

==> b = 125sin(75.5°)/sin(100°) ≈ 123.

I hope this helps!

#1